Neptune & Company

• Internship at Lakewood, CO office
• Consulting firm, founded 1992
  • Environmental Statisics
  • Bayesian decision theory/risk management
• About 50 employees around the US
• Origins with EPA

Overview

• Colorado
• Work at Neptune
• Some Environmental Statistics Topics
• Thoughts on Internships

Mt Bierstadt

Geneva City

A Local

Projects

• Environmental risk assessment
• Mathematical modeling
• Radiological performance assessment
• Unexploded ordnance cleanup
• Sampling plans
• Web-based analysis and visualization tools

A Few Sites

• Hanford Site
• Los Alamos National Lab
• Nevada Test Site
• Helena Valley

My Job – Statistics Intern

• Assist PhD statisticians
  • Analyze/plot data
  • Sampling plans
  • Writups
• Statistical methods paper
• Assist with Visual Sample Plan software
• Input on workflow/project organization

Anatomy of an Environmental Cleanup

• Statistics are just one small piece
• 80-page risk assessment becomes Appendix D of 500-page report
• Reports done in MS Word

Anatomy of an Environmental Cleanup

Anatomy of an Environmental Cleanup

Anatomy of an Environmental Cleanup

Anatomy of an Environmental Cleanup

Anatomy of an Environmental Cleanup

Upper Confidence Limits

• Regulators/risk assessors want to be “protective”
• Prefer to overestimate mean contamination concentration
• Testing mean – Reject \(H_0 \iff\) UCL > Action Level
• 95% UCL is a conservative estimate

Upper Confidence Limits

Upper Confidence Limits

Upper Confidence Limits

Upper Confidence Limits

Upper Confidence Limits

Computing (1-\(\alpha\))100% UCLs

Normal UCL

\[\bar{x}+z_\alpha\frac{s}{\sqrt{n}}\]

\(t\) UCL

\[\bar{x}+t_{n-1,\alpha}\frac{s}{\sqrt{n}}\]

Chebyshev UCL

\[\bar{x}+\sqrt{\frac{1}{\alpha}-1}\frac{s}{\sqrt{n}}\] (A. K. Singh, Singh, and Engelhardt 1997)

Computing (1-\(\alpha\))100% UCLs

• Many others have been proposed
  • Lognormal
  • Gamma
  • Skew-adjusted normal/\(t\)
  • Bootstrap

Example

Groundwater aluminium concentrations from Naval Construction Battalion Center, RI (Singh, Singh, and Iaci 2002)

• 290, 113, 264, 2660, 586, 71, 527, 163, 107, 71, 5920, 979, 2640, 164, 3560, 13200, 125
• Mean: 1849.41
• Std. Dev.: 3351.27

Which UCL Should I Use?

• Lots of confusing guidance
• Based on coverage rate, ignore bias and variance
• Error-prone goodness-of-fit tests

Which UCL Should I Use?

Non-Detects

• Data come from chemical analyses
• Labs censor values below a detection limit (DL)
• Report DL instead of result
  • We don’t have real numbers!

Problems Estimating Variability

Accounting for Non-Detects

• Simple substitutions (DL/2)
• Several MLEs
  • Must assume a distribution
• One decent nonparametric method – Kaplan-Meier (Helsel 2011)
  • Debate about implementation
• Non-detects really a data quality issue

Accounting for Non-Detects

Detection Limits are Complicated

Detection Limits are Complicated

Software and De-Facto Standards

• ProUCL developed by EPA (EPA 2016)
  • Developers involved in most UCL simulation studies
• Visual Sample Plan developed by PNNL (VSP Development Team 2016)
  • Funded by DOE
• Handful of R packages

ProUCL

VSP

A “Real Job”

• More money
• Less work
• Weekends!

A Different Learning Experience

• Expected to know statistics
  • But not “these” statistics
  • Allowed time to learn on the job
• Saw connections between policy and real-world science
• Less research